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A model for separatrix splitting near multiple resonances | | M. Rudnev
; V. Ten
; | | Date: |
13 Dec 2004 | | Subject: | Dynamical Systems; Mathematical Physics MSC-class: 70H08; 70H20 | math.DS math-ph math.MP | | Abstract: | We propose a model for local dynamics of a perturbed convex real-analytic Liouville-integrable Hamiltonian system near a resonance of multiplicity $1+m, mgeq 0$. Physically, the model represents a toroidal pendulum, coupled with a Liouville-integrable system of $n$ non-linear rotators via a small analytic potential. The global bifurcation problem is set-up for the $n$-dimensional isotropic manifold, corresponding to a specific homoclinic orbit of the toroidal pendulum. The splitting of this manifold can be described by a scalar function on an $n$-torus, whose $k$th Fourier coefficient satisfies the estimate $$O(e^{-
ho|kcdotomega| - |k|sigma}), kin^nsetminus{0},$$ where $omegainR^n$ is a Diophantine rotation vector of the system of rotators; $
hoin(0,{piover2})$ and $sigma>0$ are the analyticity parameters built into the model. The estimate, under suitable assumptions would generalize to a general multiple resonance normal form of a convex analytic Liouville integrable Hamiltonian system, perturbed by $O(eps)$, in which case $omega_jsimomeps, j=1,...,n.$ | | Source: | arXiv, math.DS/0501208 | | Services: | Forum | Review | PDF | Favorites | |
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